AOPA Pilot Magazine - January 2025 - 90

RUDDER & WRENCH
The pilot's operating handbook says after
a ground roll of 1,000 feet, the airplane will
clear a 50-foot obstacle after another 600
feet along the runway. But objects at the end
can be taller than 50 feet. Because these
nested triangles are similar, it is reasonable
to assume that after another 600 feet, or
2,200 feet in total, the airplane should be
100 feet in the air.
in the given scenario, for a departure
with a comfortable safety margin.
Surprisingly, practical exams for new
certificates aren't the only conversations
where geometry keeps coming up.
Applicants who add the instrument rating
to a current certificate must all complete a
circling approach, and knowing your way
around similar triangles can prove useful.
An instrument approach involves a
circling maneuver if the aircraft needs to
change direction significantly from the
final approach segment before landing on
the runway. Such a circling approach turns
out to be one of the sketchiest parts of an
instrument practical exam-and for good
reason. When flown low to the ground, in
poor weather conditions by a tired pilot
at the end of a long flight, it would be easy
to make a mistake that proves fatal. Pilots
should always consider other options to
conduct a straight-in approach before
choosing to circle.
It makes sense that each instrument
candidate must demonstrate circling
approach proficiency on the practical
exam. Even though the exam is often
conducted in beautiful VFR weather, the
circling approach is one of the more common
reasons I end up issuing a notice of
disapproval. The Instrument Rating
Airmen Certification Standards (FAAACS-8C)
states that, " If landing, initiate
a stabilized descent. Touch down on the
first one-third of the selected runway
without excessive maneuvering, without
exceeding the normal operating limits of
the airplane, and without exceeding 30
degrees of bank. " It's easy to argue that
a significant overshoot of the runway
centerline, and the attendant maneuvering
back to it, fails to provide a stabilized
descent. During the preflight briefing, I
remind that significantly overshooting
centerline during the circling approach
will result in a notice of disapproval. The
candidate often says, " Oh, I will maintain
a normal VFR pattern. " That's great
news and the right idea since a standard
VFR downwind leg keeps the aircraft well
within the maximum circling distance
while minimizing the risk of an overshoot.
Still, they routinely happened anyway,
so I found myself scratching my head.
I then realized that even though candidates
thought they were flying a normal
traffic pattern, they were using the wrong
reference to maintain it (see below). For
example, on the downwind leg of a typical
1,000-foot pattern altitude, keeping the
runway in the middle of the strut on my
Cessna 152, Wilbur, means that I'm about
one-half mile away from the centerline.
In my Beechcraft Bonanza, Niky, it's the
leading-edge section that resides near the
fuel cap that provides the appropriate reference.
But if the circling altitude is 500
feet agl, half of normal, and I maintain the
same reference, it means I'm half the normal
distance to the runway.
Safely turning onto base and final
within one quarter of a mile is nearly
impossible if the maximum bank angle,
as stated in the ACS, stays less than 30
degrees. For circling maneuvers, we need
to find a new reference to maintain the
normal distance from the runway on the
downwind. In Wilbur, it's about threequarters
of the way up the strut and in
Niky, the reference is just outside the
large vortex generator that protrudes forward
close to the wing tip.
I enjoy mixing mathematics and aviation
to understand what makes airplanes
fly. But when I conduct a practical exam, I
plan to keep discussions centered on aviation.
Still, the topic of similar triangles kept
coming up and sharing the topic outside of
my practical exam debriefs I hope proves
helpful for others. Catherine Cavagnaro
teaches aerobatics at UOS and is the Gaston
Swindell Bruton Professor of Mathematics
at Sewanee: The University of the South.
Airplane A flies a normal downwind of 1,000
feet. The pilot uses a point on the wing five
feet from the fuselage to ensure the distance
stays a half-mile from the runway. Airplane
B uses the same point, but in doing so, the
aircraft is only a quarter-mile away and will
overshoot the extended centerline. Airplane
C flies a normal half-mile leg using a new
reference point closer to the wing tip.
90
AOPA PILOT / January 2025
AOPA Pilot Magazine - January 2025

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